A triangle with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1) has a perimeter of 13.1 units.
A triangle is a two-dimensional shape that has three sides or edges and three vertices.
Perimeter refers to the distance around any two-dimensional shape. The perimeter of a triangle is the sum of the length of its sides.
To solve for the perimeter of triangle ABC with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1), solve first for the length of each side, namely side AB, side BC, and side AC.
And to solve for the length of each side, use the distance formula given by:
d = √(x2 - x1)^2 + (y2-y1)^2
side AB : d = √(2 - 1)^2 + (5 - 1)^2 = √1 + 16 = √17 units
side BC : d = √(5 - 2)^2 + (1 - 5)^2 = √9 + 16 = √25 = 5 units
side AC : d = √(5 - 1)^2 + (1 - 1)^2 =√16 + 0 = √16 = 4 units
Solving for the perimeter of triangle ABC,
P = AB + BC + AC
P = √17 + 5 + 4
P = 4.123 + 9
P = 13.123 units
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